Can you grow more warts if you cut open your wart?

Yes warts can spread. Do not mess with the one that you have. Go to your local drug store and get some medicine to put on it to make the wart go away. Usually if you cut it open you will get them all over the area where the other one is.

My dad once cut open a plantar's wart on his foot and said it looked like dozens of black hooks inside, he pulled them all out with a pair of tweezers and it never came back. and we threw the tweezers away.

Yes. If the skin around the area is damp, it can increase from one wart to more. But if you have cleaned the immediate area (within 2-3 inches of the wart) with alcohol, it will not spread. Then you could pop it if you liked.

Yes there is a chance to appear the warts again even if we cut off it from our body. After cutting the warts you should be careful to heal the wound by using a good antiseptic cream or such medicines and also take the medicines which can provide a good immune capacity to your body.